How can a neural network work with continuous time?
By the way you have explained things above, it seems more like a problem with your code and not the something to do with the environment. The term discrete and continuous is used to define, how the outside environment is acting, rather than how your code is taking its steps. These are some lines from the book, Artificial Intelligence: A Modern Approach:


  The discrete/ continuous distinction applies to the state of the environment, to the way time is handled, and to the percepts and actions of the agent. For example, the chess environment has a finite number of distinct states (excluding the clock). Chess also has a discrete set of percepts and actions. Taxi driving is a continuous state and continuous-time problem: the speed and location of the taxi and of the other vehicles sweep through a range of continuous values and do so smoothly over time. Taxi-driving actions are also continuous (steering angles, etc.). Input from digital cameras is discrete, strictly speaking, but is typically treated as representing continuously varying intensities and locations.


So, continuous or discrete is not something that should be talked about as a problem of the code. It is basically, what an environment is. Your concern with the device is regarding the code. I will suggest that you upload the code on git and ask people to improve it.
I hope this helps!